diff --git a/Doc/library/ipaddress.rst b/Doc/library/ipaddress.rst
index 140401d2f36739..2cdfddb02e96c4 100644
--- a/Doc/library/ipaddress.rst
+++ b/Doc/library/ipaddress.rst
@@ -487,7 +487,8 @@ dictionaries.
       hosts are all the IP addresses that belong to the network, except the
       network address itself and the network broadcast address.  For networks
       with a mask length of 31, the network address and network broadcast
-      address are also included in the result.
+      address are also included in the result. Networks with a mask of 32
+      will return a list containing the single host address.
 
          >>> list(ip_network('192.0.2.0/29').hosts())  #doctest: +NORMALIZE_WHITESPACE
          [IPv4Address('192.0.2.1'), IPv4Address('192.0.2.2'),
@@ -495,6 +496,8 @@ dictionaries.
           IPv4Address('192.0.2.5'), IPv4Address('192.0.2.6')]
          >>> list(ip_network('192.0.2.0/31').hosts())
          [IPv4Address('192.0.2.0'), IPv4Address('192.0.2.1')]
+         >>> list(ip_network('192.0.2.1/32').hosts())
+         [IPv4Address('192.0.2.1')]
 
    .. method:: overlaps(other)
 
@@ -656,6 +659,8 @@ dictionaries.
       hosts are all the IP addresses that belong to the network, except the
       Subnet-Router anycast address.  For networks with a mask length of 127,
       the Subnet-Router anycast address is also included in the result.
+      Networks with a mask of 128 will return a list containing the
+      single host address.
 
    .. method:: overlaps(other)
    .. method:: address_exclude(network)
diff --git a/Lib/ipaddress.py b/Lib/ipaddress.py
index 1014eba5517190..28b7b6159a62ef 100644
--- a/Lib/ipaddress.py
+++ b/Lib/ipaddress.py
@@ -1458,6 +1458,8 @@ def __init__(self, address, strict=True):
 
         if self._prefixlen == (self._max_prefixlen - 1):
             self.hosts = self.__iter__
+        elif self._prefixlen == (self._max_prefixlen):
+            self.hosts = lambda: [IPv4Address(addr)]
 
     @property
     @functools.lru_cache()
@@ -2110,6 +2112,8 @@ def __init__(self, address, strict=True):
 
         if self._prefixlen == (self._max_prefixlen - 1):
             self.hosts = self.__iter__
+        elif self._prefixlen == self._max_prefixlen:
+            self.hosts = lambda: [IPv6Address(addr)]
 
     def hosts(self):
         """Generate Iterator over usable hosts in a network.
diff --git a/Lib/test/test_ipaddress.py b/Lib/test/test_ipaddress.py
index 2eba740e5e7a48..2f1c5b6b6fb9c8 100644
--- a/Lib/test/test_ipaddress.py
+++ b/Lib/test/test_ipaddress.py
@@ -1124,6 +1124,15 @@ def testHosts(self):
         self.assertEqual(list(ipaddress.ip_network(str_args).hosts()),
                          list(ipaddress.ip_network(tpl_args).hosts()))
 
+        # special case where the network is a /32
+        addrs = [ipaddress.IPv4Address('1.2.3.4')]
+        str_args = '1.2.3.4/32'
+        tpl_args = ('1.2.3.4', 32)
+        self.assertEqual(addrs, list(ipaddress.ip_network(str_args).hosts()))
+        self.assertEqual(addrs, list(ipaddress.ip_network(tpl_args).hosts()))
+        self.assertEqual(list(ipaddress.ip_network(str_args).hosts()),
+                         list(ipaddress.ip_network(tpl_args).hosts()))
+
         addrs = [ipaddress.IPv6Address('2001:658:22a:cafe::'),
                  ipaddress.IPv6Address('2001:658:22a:cafe::1')]
         str_args = '2001:658:22a:cafe::/127'
@@ -1133,6 +1142,14 @@ def testHosts(self):
         self.assertEqual(list(ipaddress.ip_network(str_args).hosts()),
                          list(ipaddress.ip_network(tpl_args).hosts()))
 
+        addrs = [ipaddress.IPv6Address('2001:658:22a:cafe::1'), ]
+        str_args = '2001:658:22a:cafe::1/128'
+        tpl_args = ('2001:658:22a:cafe::1', 128)
+        self.assertEqual(addrs, list(ipaddress.ip_network(str_args).hosts()))
+        self.assertEqual(addrs, list(ipaddress.ip_network(tpl_args).hosts()))
+        self.assertEqual(list(ipaddress.ip_network(str_args).hosts()),
+                         list(ipaddress.ip_network(tpl_args).hosts()))
+
     def testFancySubnetting(self):
         self.assertEqual(sorted(self.ipv4_network.subnets(prefixlen_diff=3)),
                          sorted(self.ipv4_network.subnets(new_prefix=27)))
diff --git a/Misc/ACKS b/Misc/ACKS
index 39aa954a7b449d..4dbd7fad4c803b 100644
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -1815,6 +1815,7 @@ Jeff Wheeler
 Christopher White
 David White
 Mats Wichmann
+Pete Wicken
 Marcel Widjaja
 Truida Wiedijk
 Felix Wiemann
diff --git a/Misc/NEWS.d/next/Library/2020-03-02-23-52-38.bpo-28577.EK91ae.rst b/Misc/NEWS.d/next/Library/2020-03-02-23-52-38.bpo-28577.EK91ae.rst
new file mode 100644
index 00000000000000..de4c064378c247
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-03-02-23-52-38.bpo-28577.EK91ae.rst
@@ -0,0 +1 @@
+The hosts method on 32-bit prefix length IPv4Networks and 128-bit prefix IPv6Networks now returns a list containing the single Address instead of an empty list.